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A unified approach for novel estimates of inequalities via discrete fractional calculus techniques
Alexandria Engineering Journal ( IF 6.8 ) Pub Date : 2021-06-06 , DOI: 10.1016/j.aej.2021.04.094 Samaira Naz , Yu-Ming Chu
中文翻译:
通过离散分数阶微积分技术对不等式进行新颖估计的统一方法
更新日期:2021-08-01
Alexandria Engineering Journal ( IF 6.8 ) Pub Date : 2021-06-06 , DOI: 10.1016/j.aej.2021.04.094 Samaira Naz , Yu-Ming Chu
In this article, we introduce the discrete fractional sum equations and inequalities. Some new generalized Grüss type discrete fractional sum inequalities are developed. We employ a nabla or backward difference; we employ the Riemann-Liouville definition of the fractional difference. Furthermore, the current research is a discrete variant of fundamental inequalities set up in the recent literary works and extends a few discrete version for -fractional sum specifically on time scale , where .
中文翻译:
通过离散分数阶微积分技术对不等式进行新颖估计的统一方法
在本文中,我们介绍了离散分数和方程和不等式。开发了一些新的广义 Grüss 型离散分数和不等式。我们采用 nabla 或向后差异;我们采用分数差分的 Riemann-Liouville 定义。此外,当前的研究是在最近的文学作品中建立的基本不等式的离散变体,并扩展了一些离散版本- 特别是在时间尺度上的分数总和 , 在哪里 .